MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(x,*(x,y))
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(s(x),s(y)) -> f(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            p(s(x)) -> x
        - Signature:
            {*/2,+/2,-/2,f/2,max/2,min/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,+,-,f,max,min,p} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          *#(x,0()) -> c_1()
          *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
          +#(0(),y) -> c_3()
          +#(s(x),y) -> c_4(+#(x,y))
          -#(x,0()) -> c_5()
          -#(s(x),s(y)) -> c_6(-#(x,y))
          f#(s(x),s(y)) -> c_7(f#(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
                              ,-#(min(s(x),s(y)),max(s(x),s(y)))
                              ,min#(s(x),s(y))
                              ,max#(s(x),s(y))
                              ,*#(s(x),s(y)))
          max#(x,0()) -> c_8()
          max#(0(),y) -> c_9()
          max#(s(x),s(y)) -> c_10(max#(x,y))
          min#(x,0()) -> c_11()
          min#(0(),y) -> c_12()
          min#(s(x),s(y)) -> c_13(min#(x,y))
          p#(s(x)) -> c_14()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,0()) -> c_1()
            *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
            +#(0(),y) -> c_3()
            +#(s(x),y) -> c_4(+#(x,y))
            -#(x,0()) -> c_5()
            -#(s(x),s(y)) -> c_6(-#(x,y))
            f#(s(x),s(y)) -> c_7(f#(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
                                ,-#(min(s(x),s(y)),max(s(x),s(y)))
                                ,min#(s(x),s(y))
                                ,max#(s(x),s(y))
                                ,*#(s(x),s(y)))
            max#(x,0()) -> c_8()
            max#(0(),y) -> c_9()
            max#(s(x),s(y)) -> c_10(max#(x,y))
            min#(x,0()) -> c_11()
            min#(0(),y) -> c_12()
            min#(s(x),s(y)) -> c_13(min#(x,y))
            p#(s(x)) -> c_14()
        - Weak TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(x,*(x,y))
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(s(x),s(y)) -> f(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            p(s(x)) -> x
        - Signature:
            {*/2,+/2,-/2,f/2,max/2,min/2,p/1,*#/2,+#/2,-#/2,f#/2,max#/2,min#/2,p#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1
            ,c_5/0,c_6/1,c_7/5,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/1,c_14/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,-#,f#,max#,min#,p#} and constructors {0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          *(x,0()) -> 0()
          *(x,s(y)) -> +(x,*(x,y))
          +(0(),y) -> y
          +(s(x),y) -> s(+(x,y))
          -(x,0()) -> x
          -(s(x),s(y)) -> -(x,y)
          max(x,0()) -> x
          max(0(),y) -> y
          max(s(x),s(y)) -> s(max(x,y))
          min(x,0()) -> 0()
          min(0(),y) -> 0()
          min(s(x),s(y)) -> s(min(x,y))
          *#(x,0()) -> c_1()
          *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
          +#(0(),y) -> c_3()
          +#(s(x),y) -> c_4(+#(x,y))
          -#(x,0()) -> c_5()
          -#(s(x),s(y)) -> c_6(-#(x,y))
          f#(s(x),s(y)) -> c_7(f#(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
                              ,-#(min(s(x),s(y)),max(s(x),s(y)))
                              ,min#(s(x),s(y))
                              ,max#(s(x),s(y))
                              ,*#(s(x),s(y)))
          max#(x,0()) -> c_8()
          max#(0(),y) -> c_9()
          max#(s(x),s(y)) -> c_10(max#(x,y))
          min#(x,0()) -> c_11()
          min#(0(),y) -> c_12()
          min#(s(x),s(y)) -> c_13(min#(x,y))
          p#(s(x)) -> c_14()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,0()) -> c_1()
            *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
            +#(0(),y) -> c_3()
            +#(s(x),y) -> c_4(+#(x,y))
            -#(x,0()) -> c_5()
            -#(s(x),s(y)) -> c_6(-#(x,y))
            f#(s(x),s(y)) -> c_7(f#(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
                                ,-#(min(s(x),s(y)),max(s(x),s(y)))
                                ,min#(s(x),s(y))
                                ,max#(s(x),s(y))
                                ,*#(s(x),s(y)))
            max#(x,0()) -> c_8()
            max#(0(),y) -> c_9()
            max#(s(x),s(y)) -> c_10(max#(x,y))
            min#(x,0()) -> c_11()
            min#(0(),y) -> c_12()
            min#(s(x),s(y)) -> c_13(min#(x,y))
            p#(s(x)) -> c_14()
        - Weak TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(x,*(x,y))
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
        - Signature:
            {*/2,+/2,-/2,f/2,max/2,min/2,p/1,*#/2,+#/2,-#/2,f#/2,max#/2,min#/2,p#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1
            ,c_5/0,c_6/1,c_7/5,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/1,c_14/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,-#,f#,max#,min#,p#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,5,8,9,11,12,14}
        by application of
          Pre({1,3,5,8,9,11,12,14}) = {2,4,6,7,10,13}.
        Here rules are labelled as follows:
          1: *#(x,0()) -> c_1()
          2: *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
          3: +#(0(),y) -> c_3()
          4: +#(s(x),y) -> c_4(+#(x,y))
          5: -#(x,0()) -> c_5()
          6: -#(s(x),s(y)) -> c_6(-#(x,y))
          7: f#(s(x),s(y)) -> c_7(f#(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
                                 ,-#(min(s(x),s(y)),max(s(x),s(y)))
                                 ,min#(s(x),s(y))
                                 ,max#(s(x),s(y))
                                 ,*#(s(x),s(y)))
          8: max#(x,0()) -> c_8()
          9: max#(0(),y) -> c_9()
          10: max#(s(x),s(y)) -> c_10(max#(x,y))
          11: min#(x,0()) -> c_11()
          12: min#(0(),y) -> c_12()
          13: min#(s(x),s(y)) -> c_13(min#(x,y))
          14: p#(s(x)) -> c_14()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
            +#(s(x),y) -> c_4(+#(x,y))
            -#(s(x),s(y)) -> c_6(-#(x,y))
            f#(s(x),s(y)) -> c_7(f#(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
                                ,-#(min(s(x),s(y)),max(s(x),s(y)))
                                ,min#(s(x),s(y))
                                ,max#(s(x),s(y))
                                ,*#(s(x),s(y)))
            max#(s(x),s(y)) -> c_10(max#(x,y))
            min#(s(x),s(y)) -> c_13(min#(x,y))
        - Weak DPs:
            *#(x,0()) -> c_1()
            +#(0(),y) -> c_3()
            -#(x,0()) -> c_5()
            max#(x,0()) -> c_8()
            max#(0(),y) -> c_9()
            min#(x,0()) -> c_11()
            min#(0(),y) -> c_12()
            p#(s(x)) -> c_14()
        - Weak TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(x,*(x,y))
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
        - Signature:
            {*/2,+/2,-/2,f/2,max/2,min/2,p/1,*#/2,+#/2,-#/2,f#/2,max#/2,min#/2,p#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1
            ,c_5/0,c_6/1,c_7/5,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/1,c_14/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,-#,f#,max#,min#,p#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:*#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
             -->_1 +#(s(x),y) -> c_4(+#(x,y)):2
             -->_1 +#(0(),y) -> c_3():8
             -->_2 *#(x,0()) -> c_1():7
             -->_2 *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y)):1
          
          2:S:+#(s(x),y) -> c_4(+#(x,y))
             -->_1 +#(0(),y) -> c_3():8
             -->_1 +#(s(x),y) -> c_4(+#(x,y)):2
          
          3:S:-#(s(x),s(y)) -> c_6(-#(x,y))
             -->_1 -#(x,0()) -> c_5():9
             -->_1 -#(s(x),s(y)) -> c_6(-#(x,y)):3
          
          4:S:f#(s(x),s(y)) -> c_7(f#(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
                                  ,-#(min(s(x),s(y)),max(s(x),s(y)))
                                  ,min#(s(x),s(y))
                                  ,max#(s(x),s(y))
                                  ,*#(s(x),s(y)))
             -->_3 min#(s(x),s(y)) -> c_13(min#(x,y)):6
             -->_4 max#(s(x),s(y)) -> c_10(max#(x,y)):5
             -->_2 -#(x,0()) -> c_5():9
             -->_1 f#(s(x),s(y)) -> c_7(f#(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
                                       ,-#(min(s(x),s(y)),max(s(x),s(y)))
                                       ,min#(s(x),s(y))
                                       ,max#(s(x),s(y))
                                       ,*#(s(x),s(y))):4
             -->_2 -#(s(x),s(y)) -> c_6(-#(x,y)):3
             -->_5 *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y)):1
          
          5:S:max#(s(x),s(y)) -> c_10(max#(x,y))
             -->_1 max#(0(),y) -> c_9():11
             -->_1 max#(x,0()) -> c_8():10
             -->_1 max#(s(x),s(y)) -> c_10(max#(x,y)):5
          
          6:S:min#(s(x),s(y)) -> c_13(min#(x,y))
             -->_1 min#(0(),y) -> c_12():13
             -->_1 min#(x,0()) -> c_11():12
             -->_1 min#(s(x),s(y)) -> c_13(min#(x,y)):6
          
          7:W:*#(x,0()) -> c_1()
             
          
          8:W:+#(0(),y) -> c_3()
             
          
          9:W:-#(x,0()) -> c_5()
             
          
          10:W:max#(x,0()) -> c_8()
             
          
          11:W:max#(0(),y) -> c_9()
             
          
          12:W:min#(x,0()) -> c_11()
             
          
          13:W:min#(0(),y) -> c_12()
             
          
          14:W:p#(s(x)) -> c_14()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          14: p#(s(x)) -> c_14()
          10: max#(x,0()) -> c_8()
          11: max#(0(),y) -> c_9()
          12: min#(x,0()) -> c_11()
          13: min#(0(),y) -> c_12()
          9: -#(x,0()) -> c_5()
          7: *#(x,0()) -> c_1()
          8: +#(0(),y) -> c_3()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
          +#(s(x),y) -> c_4(+#(x,y))
          -#(s(x),s(y)) -> c_6(-#(x,y))
          f#(s(x),s(y)) -> c_7(f#(-(min(s(x),s(y)),max(s(x),s(y))),*(s(x),s(y)))
                              ,-#(min(s(x),s(y)),max(s(x),s(y)))
                              ,min#(s(x),s(y))
                              ,max#(s(x),s(y))
                              ,*#(s(x),s(y)))
          max#(s(x),s(y)) -> c_10(max#(x,y))
          min#(s(x),s(y)) -> c_13(min#(x,y))
      - Weak TRS:
          *(x,0()) -> 0()
          *(x,s(y)) -> +(x,*(x,y))
          +(0(),y) -> y
          +(s(x),y) -> s(+(x,y))
          -(x,0()) -> x
          -(s(x),s(y)) -> -(x,y)
          max(x,0()) -> x
          max(0(),y) -> y
          max(s(x),s(y)) -> s(max(x,y))
          min(x,0()) -> 0()
          min(0(),y) -> 0()
          min(s(x),s(y)) -> s(min(x,y))
      - Signature:
          {*/2,+/2,-/2,f/2,max/2,min/2,p/1,*#/2,+#/2,-#/2,f#/2,max#/2,min#/2,p#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1
          ,c_5/0,c_6/1,c_7/5,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/1,c_14/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {*#,+#,-#,f#,max#,min#,p#} and constructors {0,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE